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THE MAGNETIC MOMENT OF IRON IN
CHROMIUM AND CHROMIUM ALLOYS
L. Hedman, K. Rao, H. Åström
To cite this version:
L. Hedman, K. Rao, H. Åström.
THE MAGNETIC MOMENT OF IRON IN CHROMIUM
JOURNAL DE PHYSIQUE Colloque C6, supplement au no 8, Tome 39, aolir 1978, page (26-788
T H E MAGNETIC MOMENT OF IRON I N CHROMIUM AND CHROMIUM ALLOYS L.E. Xedman, K.V. Raot and H.U. %strEm
Department of Solid State Physics Royal Institute of Technology S-100 44 Stockholm, Sweden
Resume.- La susceptibilitd magnetique de Cr 1-3 at% Fe, Cr 2 at% Si 2-3 at% Fe et Cr 0.5-1 at%V 3 at%Fe a 4td mesurge en fonction de la tempsrature de 4,3 2 340 K. On conclut que les atomes de fer isol6s sont P l'origine de la susceptibilitd indsvendente de la temperature et que les atomes de fer voisins suivent P peu prSs la loi de Curie dans la phase commensurable.
Abstract.- The magnetic susceptibility of Cr 1-3 at% Fe, Cr 2 at% Si 2-3 at% Fe and Cr 0.5-1 at%V 3 at% Fe has been measured in the temperature region 4.3-340 K. It is inferred that isolated Fe atoms give rise to a temperature independent susceptibility and nearest neighbour Fe atoms nearly follow the Curie law in the commensurate spin-density-wave state.
In order to understand the magnetic moment of iron in chromium alloys and its interaction with the matrix and with the magnetic moments of other iron atoms, we have measured and analyzed the ma- gnetic susceptibility of the four commensurate al- loys CrZFe, Cr3Fe, CrZSiZFe and CrZSi3Fe and the three incommensurate alloys CrlFe, Cr0.5V3Fe and CrlV3Fe in the temperature region 4.3-340 K (the nominal composition given in atomic per cent). Re- sults on Cr3Fe with 0, 0.5 and 1 V have been repor- ted previously /l/, but are included here for the sake of comparison and because the analysis has been somewhat improved.
We have fitted the expression
X = (I-w)~, + A + C/(T-0) (1) with A =O, C = CH, 0 = 8 for T'TN and H A # 0, C = CL, 0 = 0 for T < T N L
to the experimental data for the magnetic mass sus- ceptibility X versus the temperature T above and below the Neel temperature TN. W is the weight frac- tion of Fe and
xm
is the susceptibility of the ma- trix (Cr, Cr2Si or Cr0.5-IV). It may be written asX,
= + B ~ T ~ (2)The constants A. and B can beunambiguouslyevalu- ated for the alloys Cr2Si2-3Fe /2/ in the whole temperature region measured and for the paramagne- tic state of the other alloys investigated /3/ for which the determination of A. and B is less accu- rate in the low temperature region (T<TN). For the comensurate alloys Cr2-3Fe, the total change
t Permanent address : Department of Physics, Clark- son College of Technology, Potsdam, New York 13676, U . S . A .
A = ~ ( 3 4 0 K)
-
.A 2nd the constant B. have been assumed to be the same as those for Cr2Si. b has also been assumed to be the same for pure Cr and the incommensurate alloys CrlFe and Cr0.5-1V3Fe. B. has been calculated from the condition
xmL =
xmH
at T = T ~ .The temperature variation of A, C and 0
L L
was investigated by fitting the expression ( I ) in various parts of the low temperature region (T<TN). It was then found that A, C and OL were indepen-
L
dent of the temperature for the commensurate alloys Cr2Si2-3Fe and Cr3Fe, but that they changed stron- gly for the incommensurate alloys CrlFe and Cr0.5-IV3Fe. CrZFe forms an intermediate case.
The accuracy of the fits is 0.1 % or better in the paramagnetic region, 0.3 % in the low tem- perature region except for T < 30 K, where it is abo-~t 3 %. The results of the fits are summarized in table I, inwhichthe weight percentage of Fe,,,, obtained by chemical analysis, and theoretical va- lues of the Curie-Weiss constant, CT, are given. C has been calculated from the well-known formula
T
where N is the number of Fe atoms per gram of tfie alloy
,
the other constants having the standard definition. It is assumed here that J=1 and g=2. An example of the fits is shown in figure I.It is assumed in the following discussion of the results shown in table I that J=1 and g=2 far at least those Fe atoms which behave in the Curie- Weiss manner. Then it is seen from eq. (3) that C is proportional to the number N of Fe atoms under consideration. Further, the concept of superpara- magnetism is invoked. For a system with N Fe atoms
distributed among ferromagnetic clusters, each con- taining n Fe atoms
CS = ( ~ / n ) ~ ~ n ~ ( n ~ + l )vzB/3~ = CT(nJ+l)/ (J+1) (4) If J=1, C =1.5C for pairs, C =2C for groups of
S T S T
three atoms, and so on. Table I
Results of fitting X = (I-W).(A +B T~)+A+c/(T-8) to
0 0
experimental X-T data for chromium alloys contai- ning dilute concentrations of iron
Alloy wt%Fe 1 0 ; ~ ~ TN Fitrange 106A 1o65 a 10% 100 w cm /g n /9\2 K K cm3l9 Kcm /g K ~ u n ~ / i Cr2Si2Fe 2.55 3.028 0.38 210 250-340 0 427.7 -67.2 458 3.119 1.30 4-170 0.987 113.2 -8.4 Cr2Si3Fe 3.50 3.208 0.38 200 250-340 0 621.4 -28.8 628 3.119 1.30 4-170 1.492 254.2 -4.5 Cr2Fe 2.39 3.246 0.55 250 270-340 0 501.3 -70.7 429 3.179 1.30 4-230 0.796 156.1 -14.3 4- 70 1.123 114.9 -7.0 80-230 0.666 203.1 -36.3 Cr3Fe 3.60 3.246 0.55 250 270-340 0 760.7 -24.1 645 3.179 1.30 4-230 1.121 347.8 -4.4 CrlFe 1.29 3.246 0.55 290 290-340 0 264.8 -122.2 231 3.124 2.00 4- 60 0.669 73.5 -12.3 70-250 0.151 160.4 -45.7 Cr0.5V3Fe 3.60 3.126 0.55 160 200-340 0 754.8 -21.6 645 2.984 6.00 4- 50 1.716 448.3 -2.9 60-170 0.462 636.9 -16.4 . CrlV3Fe 3.60 3.084 0.55 110 120-340 0 753.3 -21.3 645 2.942 12.70 4- 50 1.852 487.6 -3.4 50-110 0.019 711.7 -15.1 L
Fig. 1 : The reciprocal of =
x-(l").
(A~+B,T~)-A versus the temperature T for the alloy Cr 2.00 at% Si 3.24 at% Fe. The constants are given in table I A : low temperature fit, o : high temperature fit. In the case of Cr2Si2-3Fe alloys, CL scales as the square of the Fe concentration c. This im- plies that the term C /T-BL is due to pairs of FeL
atoms, most likely nearest neighbour ones. The small 8 value-indicates that the interaction with
L
the matrix is very small. It is probable that these nearest neighbour pairs behave superparamagnetical- ly because the direct ferromagnetic interaction between nearest neighbour Fe atomsmustbe stronger than the interaction between each Fe atom and the antiferromagnetically ordered matrix. The fraction of Fe atoms in such nearest neighbour pairs can
then be estimated as C /1.5CH, which is 18 and 27%
L
for CrZSiZFe and Cr2Si3Fe respectively. These figu- res are nearly equal to those for complete random- ness / 4 / . The A tern increases linearly with the Fe concentration and is ascribed to isolated Fe atoms, which thus give rise to a temperature inde- pendent contribution to the susceptibility in com- mensurate spin-density-waves. A possible explana-
tion of this fact is that the magnetic moments of isolated Fe atoms are frozen in the commensurate spin-density-wave structure.
If eq.(l) is fitted to the X-T data of the alloys Cr2Fe and Cr3Fe in the same low-temperature region, it is found that CL scales as c2. CL and CH are larger than those of CrZSiZFe and CrZSi3Fe. This is ascribed to the fact that J = 1.13 instead of J = 1 in the Cr-Fe alloys. The fraction of Fe atom in close pairs, CL/1.53 CH, would then be 20 and 29 % for CrZFe and Cr3Fe respectively. The fit is, however, not very good at the lowest temperatu- res for CrZFe ( 1 7 % error at 4.3 K). If the low temperature region is split into two parts as shown in Table 1, the fits become much better. The increa- se of CL in the upper part is ascribed to isolated Fe atoms, which are not frozen. The Cr2Fe alloy in- vestigated was thus not so perfectly commensurate as the other three alloys considered so far.
The data of the incommensurate alloys CrlFe, Cr0.5V3Fe and CrlV3Fe show that also most isolated Fe atoms behave in the Curie-Weiss manner and that several moments are frozen at the lowest temperatures.
This investigation has been extended to Cr- Fe alloys with Mn and Ru, which strongly increase TN. Also Cr-Fe and Cr2Si-Fe with smaller concen- trations than 1 at% Fe will be measured in order to study the behaviour of isolated Fe atoms, redu- cing the disturbing influence of nearest neighbour pairsof Fe atoms as much as possible.
ACKNOWLEDGEMENTS.- We are very grateful to Dr. Jayaraman for giving us the samples and to Prof. Friedel for enlightening discussions.
References
/l/ kstriim, H.U., Gudmundsson
.,
H., Hedman, L. and Rao, K.V., Physica86-88
(1977) 332/2/ Arajs, S., Rao, K.V., Hedman, L., and kstri;m, H.U., Low Temp. Physics, LT14 (1975) 231 /3/ Gudmundsson, H., Hedman, L., Rao, K.V. and
ftstrgrn, H.U., Proc. 23rd Int. Conf. Magnetism Magnetic Materials (to be published in J. Appl. Phys.) 1977
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